Multi-Objective OptimizatiOn in machining Of
GFRP and MMC CoMPosites: two Case
ExpErimEntal rEsEarch
Thesis Submitted in Fulfillment of the Requirements for the
Award of the Degree of
Master of technology (M.tech.)
In
Mechanical EnginEEring
(Specialization - Production Engineering)
By
Mr. VIKAS SONKAr
Roll No. 212ME2303
Under the Supervision of
DR. SAURAV DATTA
DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA 769008, INDIA
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA 769008, INDIA
Certificate of Approval
This is to certify that the thesis entitled Multi-Objective Optimization in
Machining of GFRP and MMC Composites: Two Case Experimental
Research submitted by Vikas Sonkar has been carried out under my sole
supervision in fulfillment of the requirements for the award of the Degree of
Master of Technology (M. Tech.) in Production Engineering at National
Institute of Technology, Rourkela, and this work has not been submitted
elsewhere before for any other academic degree/diploma.
------------------------------------------
Dr. Saurav Datta
Assistant Professor
Department of Mechanical Engineering
National Institute of Technology, Rourkela-769008
Acknowledgement
In pursuit of this academic endeavor I feel that I have been especially fortunate as inspiration,
guidance, direction, co-operation, love and care all came in my way in abundance and it
seems almost an impossible task for me to acknowledge the same in adequate terms.
It gives me massive pleasure to express my deep sense of gratitude to my supervisor
Prof. Saurav Datta, Assistant Professor, Department of Mechanical Engineering, NIT
Rourkela, for his valuable
guidance, motivation, constant inspiration.
provided
encouragement
me
unflinching
and
support
in
various
Above
all, he
ways
which
exceptionally inspire and enrich my growth as a student.
I am obliged to Prof. S. S. Mahapatra, Professor, Department of Mechanical Engineering,
NIT Rourkela who has inspired me with his advice and experience.
I convey regards to Prof. K. P. Maity, HOD, Mechanical Engineering, NIT Rourkela, for
their kind support and concern regarding my academic requirements.
I express my thankfulness to the faculty and staff members of the workshop specially,
Mr. Sudhansu Sekhar Samal (Technician) and Mr. Somnath Das (Technician) for CNC
Drilling during my project work.
I feel lucky to have Mr. Kumar Abhishek, Ph.D. Scholar (Production Specialization) who
worked with me in every difficulty which I have faced and his constant efforts and
encouragement was the tremendous sources of inspiration.
It‘s my pleasure to show my indebtedness to my friends Mr. Chhabi Ram Matawale,
Suman Chatterjee, Jageshwar Kumar Sahu, Sandip Kumar Sahu, Chuneshwar Lal
Verma, Johan Banjare, Yagya Sahu and Narendra Kumar Patel.
My very special thanks go to all my family members. Their love, affection and patience
made this work possible and the blessings and encouragement of my beloved parents
iii
Mr. P. R. Sonkar and Mrs. Sunita Sonkar, greatly helped me in carrying out this
research work. Special thanks to my brothers Mr. Satish Sonkar and Bhupendra Sonkar
for their infallible motivation and support.
Finally, but most importantly, I thank Almighty God, my Lord for giving me the will, power
and strength to complete my research work.
VIKAS SONKAR
iv
Abstract
Composite materials like GFRP and MMCs having more importance in various
manufacturing industries mainly in aerospace and automotive industries and many
engineering application, because of their unique mechanical properties as compare to the
conventional material. Drilling is the most common machining process in manufacturing
industries for assembly of components but drilling of composite may possesses many
difficulties such as fiber pull out, delamination and circularity etc. which affects the quality of
drilled hole. To overcome these difficulties the effect of machining parameters on different
machining responses should be investigated for attaining high product quality as well as
satisfactory machining process performance. Therefore, the main objective of this dissertation
is to investigate the various machining performance characteristics with different machining
condition in drilling of GFRP and MMCs composites by using various integrated multi
objective optimization methodologies. In this presented thesis, Deng’s similarity method
integrated with Taguchi, TOPSIS integrated with Taguchi method (in drilling of GFRP
composite) and PCA-Grey method integrated with Taguchi, Grey-TOPSIS Integrated with
Taguchi method (in drilling of MMCs), have been implemented for obtaining the optimal
machining conditions.
v
Contents
Items
Page Number
Title Sheet
i
Certificate
ii
Acknowledgement
iii - iv
Abstract
v
Contents
vii - viii
List of Tables
ix
List of Figures
x
Chapter 1: Introduction
01 - 14
1.1 Composite Materials
01
1.2 Classification of Composite Materials
02
1.2.1 According to Type of Matrix Material
02
1.2.2 According to Nature and Arrangement of the Reinforcement Phase
03
1.3 Fiber Reinforced Plastic (FRP)
04
1.4 Metal Matrix Composites (MMCs)
05
1.5 Machining Aspects of Composites: State of Art
06
1.6 Objectives of the Present Work
11
1.7 Bibliography
12
Chapter 2: Multi-Responses Optimization in Drilling of GFRP composites
15 - 28
2.1 Coverage
15
2.2 Background and Rationale
15
2.3 Experimentation
19
vi
2.4 Proposed Methodology
21
2.4.1 TOPSIS
21
2.4.2 Deng’s Similarity Based Method
23
2.5 Results and Discussions
26
2.6 Concluding Remarks
27
2.7 Bibliography
27
Chapter 3: Optimization in Drilling of Al20%SiCp Metal Matrix Composites
30 - 42
3.1 Coverage
30
3.2 Background and Rationale
30
3.3 Experimentation
33
3.4 Proposed Methodologies
34
3.4.1 PCA-Grey Integrated with Taguchi Method
34
3.4.2 Grey-TOPSIS Integrated with Taguchi Method
38
3.5 Results and Discussions
39
3.6 Concluding Remarks
41
3.7 Scope for Future Work
41
3.8 Bibliography
42
Appendix
Publications
44 - 59
60
vii
List of Tables
Table Number
Page Number
Table 2.1 Domain of Experiments
44
Table 2.2 Design of Experiment (L16) orthogonal array
44
Table 2.3 Experimental Data
45
Table 2.4 Normalized Decision Matrix
45
Table 2.5 Weighted Normalized Matrix
46
Table 2.6 Positive Ideal Solution and Negative Ideal Solution
47
Table 2.7 Conflict between each alternative and the positive and
47
the negative ideal solution
Table 2.8 Overall Performance Index (OPI)
48
Table 2.9 Corresponding S/N Ratios (of OPIs) and Predicted S/N Ratios
48
Table 3.1 Domain of Experiments
49
Table 3.2 Design of Experiments
49
Table 3.3 Experimental Data
50
Table 3.4 Normalization of Experimental Data
50
Table 3.5 Eigen value, Eigen vector, AP and CAP
51
Table 3.6 Major Principal Components for L9 experimental run
51
Table 3.7 Quality loss ( ok )
51
Table 3.8 Individual grey coefficients (  ij )
52
Table 3.9 Over all Grey coefficient ( Ri ), Corresponding S/N ratio
52
and Predicted S/N ratio
viii
Table 3.10 Corresponding S/N ratio of experimental data
53
Table 3.11 Normalized S/N ratio
53
Table 3.12 Individual Grey Coefficient
54
Table 3.13 Weighted Normalized matrix (TOPSIS)
54
Table 3.14 Positive and negative ideal solution
54
Table 3.15 Separation Distance
55
Table 3.16 Overall Performance Index (OPI) and Predicted S/N Ratio
55
ix
List of Figures
Figure Number
Page Number
Fig. 2.1 Degree of conflict between Ai and A±
23
Fig. 2.2 Degree of conflict between Ai and A+
24
Fig. 2.3 GFRP epoxy work pieces after machining
56
Fig. 2.4 Drill bits  8 , 10 used during experimentation
56
Fig. 2.5 Evaluation of optimal parametric combination by using
57
TOPSIS based Taguchi method  N 1600 f100 t 6 d 8 
Fig. 2.6 Evaluation of optimal parametric combination by using Deng’s Similarity
57
Based Method in conjugation with Taguchi approach  N 1600 f100 t 6 d 8 
Fig. 3.1 Experimental setup for drilling of Al20%SiCp Composite
58
Fig. 3.2 Evaluation of optimal parametric combination by PCA-Grey
58
integrated with Taguchi methodology
Fig. 3.3 Evaluation of optimal parametric combination by Grey -TOPSIS
59
integrated with Taguchi methodology
Fig. 3.4 Graphical comparison between PCA-Grey and Grey-TOPSIS
59
integrated with Taguchi method
x
CHAPTER 1: Introduction
1.1 Composite Materials
Composites are material made up of at least two constituent materials with significantly
different physical or chemical properties, that when combined; produce a material with
characteristics different from the individual components. The individual component remain
separate and distinct within the finished structure or we can say that composites are form by
combining two or more material together to get a desirable structure, which is better than the
individual components. Composite materials have many advantages over the conventional
metal/material like high specific strength, high specific stiffness, good corrosion resistance,
and lower coefficient of thermal expansion. But machining of the composite materials is not
an easy job; there is a remarkable difference between the machining of conventional
materials and composites because of the machining behavior of composites, which differs
one composite to other. Since it’s physical and mechanical properties depend largely on the
type of fiber, the fiber content, the fiber orientation and variability in the matrix material.
The structure of composites is made up of two phases; Matrix and Reinforcement.
Matrix: It is the constituent generally which is present in greater quantity and continuous in a
composite material. Properties of the matrix can be improved by addition of other constituent.
Reinforcement: It is the second phase of composite material and main role of this phase is to
enhance the mechanical properties of matrix phase. Generally reinforcement is harder,
stronger and stiffer than the matrix. Reinforcement can either be particulate or fibrous.
1
1.2 Classification of Composite Materials
Composite materials are mainly classified into two parts according to the phase of composite,
which are described as follows:
1.2.1 According to Type of Matrix Material
(a) Metal Matrix Composite (MMC)
(b) Ceramic Matrix Composite (CMC)
(c) Polymer Matrix Composite (PMC)
Metal Matrix Composite: As the name suggested that in this type of composite, metal is used
for matrix phase. Metal matrix composite have higher specific modulus, higher specific
strength, better properties at elevated temperatures and lower coefficient of thermal
expansion as compared to the monolithic metal. Due to this properties MMCs are used in
many application such as combustion chamber nozzle (in rocket, space shuttle), housings,
tubing, cables, heat exchangers, structural members etc.
Ceramic Matrix Composite: In this type of composite ceramic materials are used for the
matrix phase. The main motive of manufacturing ceramic composite is to improve the
toughness along with strength and stiffness of composite because of this CMCs are capable to
use in high temperature environment and highly stressed state.
Polymer Matrix Composite: Most commonly used matrix materials are polymeric. The
reasons for this are twofold. In general the mechanical properties of polymers are inadequate
for many structural purposes. In particular their strength and stiffness are low compared to
metals and ceramics. These difficulties are overcome by reinforcing other materials with
polymers. Secondly, the processing of polymer matrix composites need not involve high
pressure and doesn’t require high temperature. Also equipment required for manufacturing
polymer matrix composites are simpler. For this reason polymer matrix composites
developed rapidly and soon became popular for structural applications.
2
Composites are used because overall properties of the composites are superior to those of the
individual components for example polymer/ceramic. Composites have a greater modulus
than the polymer component but aren’t as brittle as ceramics. Two types of polymer
composites are: fiber reinforced polymer (FRP) and particle reinforced polymer (PRP).
1.2.2 According to Nature and Arrangement of the Reinforcement Phase
(a) Particulate reinforced composite
(b) Fiber reinforced composites
(c) Hybrid composite
(d) Laminated composite
Particulate Reinforced Composite: It is the composite in which reinforcement is used in
form of particulate with approximate equally distributed in all dimension of composite.
Particulate reinforcement is used to high temperature performance, reduce friction, improve
wear resistance and to reduce shrinkage. Particulate reinforcement is improve stiffness
effectively but unable to provide strength to composite.
Fiber Reinforced Composites: Composite in which reinforcements having lengths higher
than cross sectional dimension is called as fiber reinforced composite. Length of the
reinforcing fiber in a single layer composite may be long or short, it depends on its overall
dimensions. Composite with long fibers, oriented in one direction is known as continuous
fiber reinforcement. These oriented fibers are enhancing composites strength. Composite with
the short reinforced fibers is known as discontinuous fiber reinforcement. Length of fibers are
neither too short to loss their fibrous nature nor too long to entangle with each other.
Hybrid Composite: composite in which two or more different types of particulates or mostly
fibers used as filler in a single matrix are called hybrid composite. Due to hybridization
properties of composites are improved and also it becomes economical. Composite with
polymeric resin as the matrix and both glass and carbon fibers as reinforcing phase is the
3
most commonly used hybrid composite. Because of hybridization of composites it is possible
get anisotropic properties in most of the hybrid composites easily. Generally the overall
properties of a hybrid composite are better than the composites having only one fiber as
reinforcing phase.
Laminated Composite: It is made up by bonding a number of laminates in thickness
direction. Generally three layers are arranged alternatively for better bonding between
reinforcement and the polymer matrix, for example plywood and paper.
1.3 Fibre Reinforced Plastic (FRP)
Fiber reinforced polymer (FRP) composite is made up of a polymer matrix (it may be either a
thermoplastic or thermoset resin, such as polyester, vinyl ester, epoxy, phenolic) incorporated
with a reinforcing material like glass, carbon, aramid and boron etc. which have sufficient
aspect ratio (length to thickness) to provide a discernable reinforcing function in one or more
directions. Some times in FRP composite core materials and additives are also added to
improve properties of the final product. During machining of FRP composites many
problems arises such as fiber pull-out, burr, delamination and burning etc. it is due to the nonhomogeneity of the constituent of the composite materials. GFRP (Glass Fiber Reinforced
Plastic) composites are the most common used FRP composites. The main advantage of
GFRP is its low cost, high tensile strength, high chemical resistance and excellent insulating
properties. FRP composites also have the capability of good resistance to creep (permanent
deflection under long term loading) and prevent the rapid propagation of cracks as in metals.
Advantages of FRP Composites
a) Lighter weight
b) The design can be optimized to meet stiffness, strength and manufacturing requirements
c) Part consolidation to provide pre-fabricated/pre-assembled product
4
d) Complex shapes are easily accomplished
e) Corrosion resistance
f) Resistant to fatigue damage with good damping characteristics
1.4 Metal Matrix Composites (MMCs)
In composites, when a metal is used as matrix phase then composite is called as metal matrix
composite (MMC). Due to the metal matrix, MMCs can be distinguished from conventional
metal in terms of increased strength, higher elastic modulus, high temperature sustainability,
improved abrasion and wear resistance, high electrical and thermal conductivity, lighter
weight and low coefficient of thermal expansion. These properties of MMCs can be
controlled by the proper choice of matrix and reinforcement. Generally metal matrix serves
the function of proper distribution and transfer of load to the reinforcement. Because of these
properties MMCs are used in typical applications such as fabrication of satellite, missile,
helicopter structures, structural support, piston, sleeves and rims, high temperature structures,
drive shaft, brake rotors, connecting rods, engine block liners various types of aerospace and
automotive applications etc.
Aluminum is the most common metal matrix material used as a structural design especially in
the aerospace industry because of its light weight properties. Aluminum having low strength
as well as low melting point therefore we can’t able to use only Aluminum metal as structural
material. This problem can be solved by using Aluminum as matrix material with a
reinforced element such as SiC particles and whiskers. Mostly SiC particles are used as
reinforcement purpose because of its having many advantages over the various reinforcement
material such high modulus and strengths, excellent thermal resistance, good corrosion
resistance, good compatibility with the Aluminum matrix, low cost and ready availability. In
industrial applications, Aluminum alloy-based composites with silicon carbide reinforcement
5
have created significant interest due to its high-strength, high-specific modulus and low
density.
Advantages and Disadvantages of MMC
Compared to monolithic metals, PMC and CMCs, MMCs have:
a) Higher strength-to-density ratio and stiffness-to-density ratios.
b) Better fatigue resistance and lower creep rate.
c) Better elevated temperature properties.
d) Lower coefficients of thermal expansion.
e) Better wear resistance and radiation resistance.
f) Higher temperature capability with fire resistance.
g) Higher transverse stiffness and strength.
h) No moisture absorption and no outgassing.
i) Higher electrical and thermal conductivities.
j) Fabricability of whisker and particulate-reinforced MMCs with conventional metal
working equipment.
Some of the disadvantages of MMCs compared to monolithic metals, PMCs and CMCs are
a) Higher cost of some material systems.
b) Relatively immature technology.
c) Complex fabrication methods for fiber-reinforced systems (except for casting).
d) Limited service experience.
1.5 Machining Aspects of Composites: State of Art
Composites offer higher stiffness and specific strength than that of conventional structural
metals and are immensely being used in aerospace and automotive industries. Composites
mainly comprises of light weight metal as matrix element, and the fibers, whiskers or
6
particles as the reinforcing elements. Out of several composites, MMCs and FRP composites
gained more attraction nowadays particularly in aerospace and automotive industries due to
their light in weight, high specific strength and high stiffness. Hence, it became a challenge
for manufacturers to study the machinability aspects of these composites. A lot of research
has been carried out over the past years to study the machinability of composites using
traditional machining methods such as turning, drilling etc. and reported considerable
improvement in dimensional and performance characteristics like surface roughness, hole
quality as well as tolerance.
Ramulu et al. (2002) studied the behavior of process parameter on machining Al2O3
aluminum-based metal matrix composites using different drills (high-speed steel, carbidetipped, and polycrystalline diamond (PCD) drills). The drilling characteristics were evaluated
in terms of drilling forces, tool wear, chip formation, and drilled-hole quality. It was found
that PCD drills outperformed all other drills in terms of drilled-hole quality and minimum
drilling forces induced. Tosun and Muratoglu (2004) experimentally examined the influence
of the type of drills, point angles of drills and ageing on the drilling performance of 2124
Aluminum alloy reinforced with 17% SiC particulates. The experiments were conducted
under different settings of parameters: spindle speed, feed rate and point angles of drill by
using high-speed steel (HSS), TiN coated HSS and solid carbide drills. It was found that the
effect of point angles on the sub-surface damage caused by the drilling operation was
changed with the type of drills. Hocheng et al. (2005) investigated the delamination effect (at
entrance and exit) of the drilled hole due to anisotropy and non-homogeneity of composite
materials and also attempted to find the way of delamination-free drilling of composite
material. Arul et al. (2006) conducted drilling experiments on GFRP with plain HSS, TiN
coated HSS and tipped tungsten carbide drills. The authors found that most of the drilling
defects were causing due thrust force.
7
Sardinas et al. (2006) proposed a multi-objective optimization methodology of the drilling
process on a laminate composite material. A micro-genetic algorithm posteriori approach was
used to investigate the effect of drilling parameters on material removal rate and delamination
factor. Singh et al. (2006) focused to correlate drilling-induced damage with drilling
parameters. Here tool point geometry was taken as the major input parameter. Along with
tool geometry, cutting speed and feed rate were found also responsible for the drilling
induced damage. A model was developed for evaluation of thrust, torque, and damage. In
another paper, Singh et al. (2008) investigated the effects of drilling parameters on the output
responses viz. thrust force and torque. Experiments were conducted and the results of
ANOVA were used in developing a Finite Element model for predicting drilling induced
damage. Haq et al. (2008) implemented an efficient approach for the optimization of drilling
parameters on drilling Al/SiC metal matrix composite with multiple responses based on
orthogonal array with grey relational analysis. Drilling parameters viz. cutting speed, feed
and point angle were optimized with the considerations of multi-responses such as surface
roughness, cutting force and torque.
Basavarajappa et al. (2008) concentrated on the
influence of cutting parameters on thrust force, surface finish, and burr formation in drilling
Al2219/15SiCp and Al2219/15SiCp-3Gr composites fabricated by the liquid metallurgy
method. The tools used were commercially available carbide and coated carbide drills. The
results revealed that feed rate had a major influence on thrust force, surface roughness, and
exit burr formation. Graphitic composites exhibited lesser thrust force, burr height, and
higher surface roughness when compared to the other material and it was due to the solid
lubricating property of the graphite particles. The higher surface roughness value for
Al2219/15SiCp-3Gr composite was due to the pullout of graphite from the surface. Karnik et
al. (2008) analyzed delamination behavior as a function of drilling process parameters at the
entrance of the CFRP plates. The effect of spindle speed, feed rate and point angle had been
8
found on the response delamination by developing an artificial neural network (ANN) model.
Drilling experiments were carried out with cemented carbide (grade K20) twist drills. The
results of ANN models and measured value were compared to verify the effectiveness of
model to predicting delamination factor. Krishnaraj et al. (2008) carried out drilling
experiments with different drill bits, namely standard twist drill, Zhirov-point drill, and
multifacet drill by taking spindle speed and feed rate as input parameters to analyze the
output responses such as thrust force, delamination and surface roughness. It was found that
delamination was less while a multi facet drill was used. Latha et al. (2009) conducted
drilling tests on GFRP composite specimens using solid carbide drill bits. A L27 orthogonal
array was used for these tests. A fuzzy rule based model was developed to predict the
delamination in drilling of GFRP composites. The proposed fuzzy rule based model could be
used effectively for predicting the delamination in drilling GFRP composites. Dhavamani and
Alwarsami (2012) emphasized to determine the optimum machining condition for
maximizing metal removal rate and minimizing the surface roughness in drilling of
Aluminum Silicon Carbide (AlSiC) by using Desirability Function (DF) approach. Taguchi
method with an L27 design was selected for the experiment to obtain the optimal settings of
factors and their effects on multiple performance characteristics. Analysis of Variance
(ANOVA) was performed to verify the fit and adequacy of the developed mathematical
models. A multiple regression model was used to represent relationship between input and
output variables and a multi-objective optimization method based on a Genetic Algorithm
(GA) was used to optimize the process. Kumar et al. (2012) examined the drilling
characteristics of GF/vinyl ester composites. Drilling forces and the surface roughness were
analyzed with input parameters such as drill geometry, the cutting speed and the feed rate.
ANOVA analysis was performed and the results of the experimental investigation showed
some important facts of the drilling behavior of GF/vinyl ester composites filled with fillers.
9
Mayyas et al. (2012) used multiple regression analysis (MRA) and artificial neural networks
(ANN) in order to investigate the influence of some parameters on the thrust force and torque
in the drilling processes of self-lubricated hybrid composite materials. In this model cutting
speed, feed, and volume fraction of the reinforcement particles were used as input data and
the thrust force and torque as the output data. ANNs showed better predictability results
compared to MRA due to the nonlinearity nature of ANNs. The statistical analysis
accompanied with artificial neural network results showed that Al2O3, Gr and cutting feed (f)
were the most significant parameters on the drilling process, while spindle speed seemed
insignificant. Abhishek et al. (2013) adopted response surface methodology to highlight the
effect of machining parameters such as spindle speed, feed rate and depth of cut on
machining evaluation characteristics viz. MRR, surface roughness and tool-tip temperature
during the turning of CFRP composites. The research also developed a mathematical model
for aforesaid characteristics to predict these performance responses on the machining of
CFRP composites. Karimi et al. (2013) investigated the effect of various drilling parameters
on thrust force, adjusted delamination factor and compressive residual strength of unidirectional glass/epoxy resin. Experimental results showed the feed rate was the most
influencing parameter for output responses. The Acoustic Emission (AE) technique was used
to observer both drilling process and compression test. The results revealed that root mean
square (RMS) could be used for monitoring thrust force and AE energy for compression
force. Raj et al. (2013) concentrated on evaluation of thrust force and surface roughness in
drilling of Al/15%Sic/4% Graphite hybrid metal matrix composite fabricated using Stir
casting method. The experiments were conducted to optimize the spindle speed and feed rate
for the output performance parameters namely thrust force and surface roughness using
coated carbide twist drill and carbide multifaceted drills under various cutting conditions.
From the experimental results it was found that the feed rate had a major influence on thrust
10
force and surface roughness. Shivapragash et al. (2013) focused on multiple response
optimization of drilling process for composite Al-TiBr2 to minimize the damage events
occurring during drilling process. Taguchi method with grey relational analysis was used to
optimize the machining parameters with multiple performance characteristics in drilling of
MMC Al-TiBr2. It was found that the maximum feed rate, low spindle speed were the most
significant factors which affected the drilling process; the performance of the drilling process
could be effectively improved by using this approach.
1.6 Objectives of the Present Work
1. To investigate on parametric appraisal and multi-response optimization in drilling of
composites (GFRP and MMC).
2. To study Taguchi based integrated optimization methodologies and their application
feasibility for machining performance optimization during drilling of GFRP/MMC
composites.
3. To compare performance (predicted optimal setting) of Deng’s Similarity Method, PCAGrey, Grey-TOPSIS (each combined with Taguchi’s philosophy) for simultaneous
optimization of multi-performance-yields during drilling of GFRP/MMC composites.
11
1.7 Bibliography
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Arul S, Vijayaraghavan L, Malhotra SK and Krishnamurthy R (2006) Influence of Tool
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Basavarajappa S, Chandramohan G, Davim JP, Prabu M, Mukund K, Ashwin M and Kumar
MP (2008) Drilling of Hybrid Aluminium Matrix Composites, International Journal
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12
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13
Singh I and Bhatnagar N (2006) Drilling of Unidirectional Glass Fiber Reinforced Plastic
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Response Optimizations in Drilling using Taguchi and Grey Relational Analysis,
International Journal of Modern Engineering Research, 3(2): 765-768.
Tosun G and Muratoglu M (2004) The Drilling of an Al/SiCp Metal-Matrix Composites, Part
I: Microstructure, Composites Science and Technology, 64(2): 299-308.
14
CHAPTER 2: Multi-Responses Optimization in Drilling of GFRP composites
2.1 Coverage
Composite materials have been gaining immense importance in manufacturing industries,
particularly in aerospace and automotive industries, due to their excellent properties as
compared to other conventional metals. In manufacturing sector, drilling is a very common
machining operation; whilst drilling of glass fiber reinforced polymer (GFRP) composite is
substantially different from metallic materials due to fiber delamination, fiber pull-out etc. In
order to produce satisfactory product quality (GFRP drilled hole), investigations on
machining and machinability aspects of GFRP composites are indeed essential.
Understanding of the effect of process variables viz. drill speed, feed rate, drill diameter,
plate thickness etc. is very important in order to select optimal machining condition towards
improving overall machining performance. Therefore, this work focuses on the analysis of
drill force (thrust), torque, surface roughness (Ra) and delamination behavior (of the drilled
hole) as a function of drilling process parameters. The unified aim of this work is to
determine an optimal machining environment based on the concept of the ‘Degree of
Similarity Measure’ between each alternative and the ideal solution using alternative gradient
and magnitude; TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and
Deng’s solution.
2.2 Background and Rationale
In recent years, GFRP composite materials are widely being used in various engineering
applications such as automobile, aerospace industries, spaceship and sea vehicle industries
because of their unique properties such as high specific stiffness, high specific strength, high
specific modulus of elasticity, high damping capacity, good corrosion resistance, good
15
tailoring ability, excellent fatigue resistance, good dimensional stability and a low coefficient
of thermal expansion. In aforesaid fields, drilling of GRFP composite materials is a common
machining operation.
During drilling of composite materials many problems arise like fiber pull-out, delamination,
stress concentration, swelling, burr, splintering and micro cracking etc. which are likely to
reduce machining performance. Amongst various defects, delamination (at entrance and exit
of the plane of the work piece) is the most critical. Delamination can result in lowering of
bearing strength and can be detrimental to the material durability by reducing the inservice life under fatigue loads. Delamination during drilling is due to compressive thrust
force acting on the uncut portion and peeling force acting on the cut portion. Past
investigations showed that the thrust force is the major factor which is responsible for the
delamination induced during the drilling GFRP and it mainly depends on the drill materials,
drill geometry and feed rate. Many of the research work focused on the behavior of drilling
process parameters on machining and machinability aspects of a variety of composite
materials.
Davim et al. (2004) established a correlation between cutting velocity and feed rate with the
specific cutting pressure, thrust force, damage factor and surface roughness, in a GFRP
material. A plan of experiments based on the Taguchi technique was established considering
drilling with prefixed cutting parameters in a hand lay-up GFRP material. The analysis of
variance (ANOVA) was performed to investigate the cutting characteristics of GFRP’s using
Cemented Carbide (K10) drills. Langella et al. (2005) presented a mechanistic model for
predicting thrust and torque during composite materials drilling. The authors specified the
number of coefficients to be experimentally determined and provided a detailed analysis of
the problems associated with the action of the chisel edge. They concluded that the model
afforded a focused approach to the definition of the most appropriate drill geometry and
16
cutting parameters in composite materials drilling. Singh et al. (2009) conducted experiments
by using 8 facet solid carbide drills based on L27 Orthogonal Array (OA). The process
parameters investigated were spindle speed, feed rate and drill diameter. Fuzzy rule based
model was developed to predict thrust force and torque in drilling of GFRP composites. The
results indicated that the model could be effectively used for predicting the response variable
by means of which delamination could be controlled. Kilickap et al. (2010) investigated the
influence of the cutting parameters, such as cutting speed and feed rate, and point angle on
delamination produced while drilling a GFRP composite. This work focused on the
application of Taguchi method and analysis of variance (ANOVA) for minimization of
delamination influenced by drilling parameters and drill point angle. The conclusion revealed
that feed rate and cutting speed were the most influential factor on the delamination,
respectively. The best results of the delamination were obtained at lower cutting speeds and
feed rates. Latha et al. (2011) studied the influence of drill geometry on thrust force in
drilling GFRP composites. Drilling experiments were conducted on composite materials
using CNC drilling machine. The response analyzed was thrust force. The influence of drill
geometry on thrust force in drilling of composite materials was carried out using three
different drill bits, namely, ‘Brad and Spur’ drill, ‘multifaceted’ drill, and ‘step’ drill. The
analyses of the experimental results were carried out using effect graphs and three
dimensional graphs. The results indicated that the step drills were performing better than the
other drills considered. Palanikumar (2011) proposed an approach for optimization of drilling
parameters with multiple performance characteristics based on the Taguchi’s L16, 4-level
orthogonal array design with grey relational analysis. Spindle speed and feed rate were the
drilling parameters and the process was optimized with consideration of multiple
performance characteristics, such as thrust force, surface roughness and delamination factor.
The analyzed grey results indicated that feed rate was the most influencing parameter than the
17
spindle speed. Verma et al. (2011) proposed a fuzzy rule based model combined with
Taguchi philosophy to determine the favorable machining condition for FRP composite
machining thereby satisfying the conflicting criteria MRR and surface roughness
simultaneously.
Tsao et al. (2012) proposed a novel method for the reduction of delamination during
composite drilling by active backup force. The applied backup force contributed to
suppression of the growth of the delamination at drilling exit by 60-80%. The proposed novel
drilling technique revealed the potential for fabrication of composite components at low cost
and minor delamination with high feed rate. Krishnamoorthy et al. (2012) used Taguchi’s L27
orthogonal array to perform drilling of CFRP composite plates. Grey relational analysis was
used to get the optimal combination of drilling parameters. Output performance parameters
such as thrust force, torque, entry delamination, exit delamination and eccentricity of the
holes were taken as criteria for analysis of drilled hole. ANOVA was used for analysing the
input parameters and found that feed rate was the most influential factor in drilling of CFRP
composites. Kumar et al. (2013) concentrated on the multi-performance optimization on
machining characteristics of unidirectional glass fiber reinforced plastic (UD-GFRP)
composites. The Distance-Based Pareto Genetic Algorithm (DPGA) was used to optimize the
cutting condition. Tool rake angle, tool nose radius, feed rate, cutting speed, cutting
environment (dry, wet and cooled) and depth of cut were used as cutting parameters for the
output responses. Okutan et al. (2013) developed machine force equations in the drilling of
[0°/+45°/90°/–45°] oriented GFRP with the help of Shaw and Oxford model. Experiments
were conducted on the GFRP samples using 118° point angle drills under dry conditions.
Input parameters: feed rate and drill diameter were analyzed on the output responses such as
torque and thrust force by using mathematical models. Measured and calculated data were
comparing to each other to verify the accuracy of the developed model.
18
The objective of the present study is to investigate the effect of the machining variables viz.
drill speed, feed rate, drill diameter along with plate thickness (work piece) on the output
performances like thrust force, torque, delamination factor and surface roughness (of the
drilled hole) during drilling GFRP composites. Based on experimental results, an optimum
design of cutting variables (optimal parameter setting) has been obtained by using Deng’s
similarity measure method in conjugation with Taguchi’s optimization philosophy. Results
obtained thereof, have been compared with that of TOPSIS.
2.3 Experimentation
Experimental Setup
Experiments have been executed on CNC drilling machine [MAXMILL 3 axis CNC machine
with FANUC Oi Mate MC Controller, Model No. CNC 2000EG].
Design of Experiment (DOE)
Design of Experiment comprises of set of experiments which are to be carried out in a
sequential manner for evaluating the response measurements. Taguchi’s orthogonal array
design of experiment is an economic as well as effective method to examine the effects of the
machining parameters through limited number of experiments. The present study focused on
the effects of drilling parameters such as drill speed, feed rate and thickness of the composite
plates; each varied in four different levels, whereas, drill diameter has been varied in two
different levels (as shown in Table 2.1) on different machining performance features namely
thrust force, torque, entry-exist delamination factor and surface roughness of the drilled hole.
In this experimentation, mixed level L16 orthogonal array has been used as shown in Table
2.2.
19
Work Piece and Tool material
GFRP epoxy composite samples of varying thickness (Fig. 2.3) have been used for execution
of the experimentation. TiAlN coated solid Carbide drill bits [Manufacturer: WIDIA-Hanita,
Product: M1308000RT] of different size such as 8 mm and 10 mm have been used for
performing drilling as shown in Fig. 2.4.
Machining Performance Characteristics
Drilling operation has been carried out on GFRP composites for assessing performance
characteristics such as load, torque, entry delamination factor, exit delamination factor as
well as surface roughness of the drilled hole.
Thrust force and torque has been evaluated by using Digital Drilling Tool Dynamometer
[Make: Medilab Enterprises, Chandigarh, INDIA], whereas, entry delamination factor and
exit delamination factor has been assessed by using formula given below:
Fd  Dmax
d
(2.1)
Where,
Fd
= delamination factor,
D max = maximum diameter observed in the damaged zone,
d = diameter of the drill.
Here, Surface Roughness Tester SJ-210 (Make: Mitutoyo) has been used to measure the
roughness average value based on carrier modulating principle.
20
2.4 Proposed Methodology
2.4.1 TOPSIS
The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method was
firstly proposed by (Hwang and Yoon, 1981) for assessing the alternatives before the
multiple-attribute decision making. TOPSIS is implemented to measure the extent of
closeness to the ideal solution. The basic concept of this method is that the chosen alternative
should have the shortest distance from the positive ideal solution and the farthest distance
from negative ideal (anti-ideal) solution. Positive ideal solution is the composition of the best
performance values demonstrated (in the decision matrix) by any alternative for each
attribute. The negative-ideal solution is the composition of the worst performance values. The
steps involved for calculating the TOPSIS values are as follows:
Step 1:
Development of decision Matrix: The row of this matrix is allocated to one
alternative and each column to one attribute. The matrix can be expressed as:
A1  x11

A2  x 21
.  .
D 
Ai  xi1
.  .

Am  xm1
x12
x22
. x1 j
. x2 j
.
.
.
xi 2
.
.
.
xij
.
xm 2
. xmj
x1 n 
x2 n 
. 

. 
. 

xmn 
(2.2)
Here, Ai ( ( i  1, 2, .......,m ) represents the possible alternatives; x j  j  1, 2 , ........,n  represents
the attributes relating to alternative performance, j  1, 2,.........., n and xij is the performance
of Ai with respect to attribute X j .
Step 2: Obtain the normalized decision matrix rij .This can be represented as:
rij 
xij
(2.3)
m
x
2
ij
i 1
21
Here, rij represents the normalized performance of Ai with respect to attribute X j .
Step 3: obtain the weighted normalized decision matrix, Y  y ij  can be found as:
Y  w j rij
 y11
y
 21
 .
Y 
 y i1
 .

 y m1
y12
y 22
. y1 j
. y2 j
.
.
.
yi2
.
.
.
yij
.
ym 2
. y mj
y1n 
y 2 n 
. 

. 
. 

y mn 
(2.4)
n
w
Here,
j
1
j 1
Step 4: Determine the ideal (best) and negative ideal (worst) solutions:
a) The ideal solution:


A   max y ij j  J , min y ij j  J ' i  1, 2 , .........., m
i
i

 y 1 , y 2 ,........, y j ,.....y n

(2.5)

b) The negative ideal solution:


A   min y ij j  J , max y ij j  J ' i  1, 2 , ........,m
i

i
 y 1 , y 2 ,........, y j ,.... y n

(2.6)

Here,
J   j  1,2 ,.......,n j : Associated with the beneficial attributes
J '   j  1,2 ,.......,n j : Associated with non-beneficial attributes
Step 5: Determine the distance measures. The separation of each alternative from the ideal
solution is given by n- dimensional Euclidean distance from the following equations:
n
S i 
 y
ij
 y j

2
i  1, 2, .........,m
(2.7)
j 1
22
n
S i 
 y
ij
 y j

2
i  1,2 , .........,m
(2.8)
j 1
Step 6: Calculate the Overall performance coefficient closest to the ideal solution:
C i 
S i
, i  1, 2,........., m; 0  C i  1
S i  S i
(2.9)
2.4.2 Deng’s Similarity Based Method
Deng’s similarity-based method is a modified form of TOPSIS methodology based on concept
that ideal solution is used in such manner so that most preferred alternative should have the
highest degree of similarity to the positive ideal increasing or decreasing values. It proposed
for evaluating the conflicting index between two alternatives to show the degree conflict
between the alternatives (Safari et al., 2013; Refer Fig. 2.1-2.2).
Fig. 2.1: Degree of conflict between Ai and A±
23
Fig. 2.2: Degree of conflict between Ai and A+
Steps involved in Deng’s Similarity-Based Method
Step 1: Formulation of decision matrix
Step 2: Normalization of decision matrix
Step 3: Determination of weighted decision matrix
Step 4: Evaluation of Positive ideal and negative ideal solution
Step 5: Estimation of conflict between each alternative and the positive and the negative ideal
solution:
Ai , A   Ai A  cos  
(2.10)
Ai , A    y ij y j 
(2.11)
 m 2
Ai    y ij 
 j 1

 m

A    y ij 2 
 j 1

0 .5
(2.12)
0 .5

(2.13)
m
y
cos  i 
ij
y j
j 1

2 
  y ij 


 j 1

m
0.5
 m 2 
  y ij 


 j 1

0.5
(2.14)
24
m
y
cos  i 
ij
y j
j 1

2
  y ij 


 j 1

m
0 .5
 m 2 
  y ij 


 j 1

(2.15)
0 .5
Step 6: Assessment of the degree of similarity between each alternative and the positive and
the negative ideal solution
C i  cos  i   Ai
(2.16)
m
y
Ci 
S

i
ij
y j 
j 1
 m '2
  yij 


 j 1


Ci
A 

0.5
 m  2 
  y ij 


 j 1

0 .5
cos     A1
A 
 m 2
   y ij 
 j 1

cos 


0 .5
(2.17)
2
 m


  y ij 
 j 1



 m 2 
  y ij 


 j 1

0 .5
0 .5
(2.18)
Step 7: Evaluation of overall performance index:
Pi 
S i
, i  1,2 ,........,n
S i  S i
(2.19)
Step 8: Determine the optimum process variable by optimization OPI using Taguchi method
The optimum process parameter combination ensures highest OPI value. The closeness
coefficient value is optimized using Taguchi method. For calculating S/N ratio
(corresponding to the values of closeness coefficient); Higher-the-Better (HB) criterion is to
be considered. As larger the value of closeness coefficient, better is the proximity to the ideal
solution.
25
2.5 Results and Discussions
Experimental data presented in Table 2.3 have been analyzed by following aforesaid
procedures. Two different techniques have been applied utilizing these output response
characteristics. Individual experimental runs (parameters settings) have been dealt as the
alternatives and the normalized decision matrix have been calculated and presented in the
Table 2.4. Assuming equal priority weight of the responses (20%), the weighted normalized
matrix has thus been computed and presented in Table 2.5. According to TOPSIS philosophy,
the positive ideal and negative-ideal solutions have been determined and shown in Table 2.6.
The degree of conflict between each alternative and the positive and the negative ideal
solution has been determined and tabulated in Table 2.7. Table 2.8 presents the overall
performance coefficient that has been evaluated by using all these two methodologies:
TOPSIS and Deng’s similarity method.
Finally, the Taguchi method has been applied on the overall performance coefficient (OPI) to
assess the optimal machining parameter by using S/N ratio plot of OPI. Higher the value of
closeness coefficient, the corresponding parameter combination is said to be close to the
optimal solution. Fig. 2.5-2.6 show the optimal parametric combination obtained by these
different methodologies and it has been noticed that predicted S/N ratios values for these
optimal combination individually represent highest value than that obtained for
corresponding S/N ratios as depicted in Table 2.9.
26
2.6 Concluding Remarks
The present study investigates the influence of drilling parameters based on parametric
appraisal and optimization (minimization) of thrust forces, torque, surface roughness, damage
factor and thereby attaining defect controlled drilling of GFRP composites using TiAlN
coated solid Carbide drill bits, according to the L16 orthogonal array experiments. Optimal
parametric combination obtained from TOPSIS and Deng’s similarity methods are found
similar to each other. Experimental approach illustrates the feasibility and effectiveness of
these proposed methodologies for optimizing the drilling parameters to achieve better quality
holes in GFRP composites.
2.7 Bibliography
Abhishek K, Datta S, Mahapatra SS, Mandal G, Majumdar G (2013) Taguchi approach
followed by fuzzy linguistic reasoning for quality-productivity optimization in
machining operation: A case study, Journal of Manufacturing Technology
Management, 24(6): 929-951.
Davim JP, Reis P, Antonio CC (2004) Experimental Study of Drilling Glass Fiber Reinforced
Plastics (GFRP) Manufactured by Hand Lay-up, Composites Science and
Technology, 64(2): 289-297.
Kilickap E (2010) Optimization of Cutting Parameters on Delamination Based on Taguchi
Method during Drilling of GFRP Composite, Expert Systems with Applications,
37(8): 6116-6122.
Krishnamoorthy A, Boopathy SR, Palanikumar K and Davim JP (2012) Application of Grey
Fuzzy Logic for the Optimization of Drilling Parameters for CFRP Composites with
Multiple Performance Characteristics, Measurement, 45(5): 1286-1296.
27
Kumar S, Meenua and Satsangib PS (2013) Multiple Performance Optimization in Machining
of Ud-GFRP Composites by a PCD Tool using Distance – Based Pareto Genetic
Algorithm (DPGA), Mechanica Confab, 2(2): 49-66.
Langella A, Nele L and Maio A (2005) A Torque and Thrust Prediction Model for Drilling of
Composite Materials, Composites: Part A, 36(1): 83-93.
Latha B, Senthilkumar VS and Palanikumar K (2011) Influence of Drill Geometry on Thrust
Force in Drilling GFRP Composites, Journal of Reinforced Plastics and Composites,
30(6): 463-472.
Okutan E, Karabay S, Sınmazçelik T and Avcu E (2013) A Study on the Derivation of
Parametric Cutting Force Equations in Drilling of GFRP Composites, Journal of
Mechanical Engineering, 59(2): 97-105.
Palanikumar K (2011) Experimental Investigation and Optimisation in Drilling of GFRP
Composites, Measurement, 44(10): 2138-2148.
Panda SS, Singh AK, Chakraborty D and Pal SK (2006) Drill Wear Monitoring using Back
Propagation Neural Network, Journal of Materials Processing Technology, 172(2):
283–290.
Safari H, Khanmohammadi E, Hafezamini A and Ahangari SS (2013) A New Technique for
Multi Criteria Decision Making Based on Modified Similarity Method, Middle-East
Journal of Science and Research, 14(5): 712-719.
Singh RVS, Latha B and Senthilkumar VS (2009) Modeling and Analysis of Thrust Force
and Torque in Drilling GFRP Composites by Multi-Facet Drill Using Fuzzy Logic,
International Journal of Recent Trends in Engineering, 1(5): 66-70.
Tsao CC, Hocheng H and Chen YC (2012) Delamination Reduction in Drilling Composite
Materials by Active Backup Force, CIRP Annals - Manufacturing Technology, 61(1):
91-94.
28
Verma RK, Abhishek K, Datta S and Mahapatra SS (2011) Fuzzy Rule Based Optimization
in Machining of FRP Composites, Journal of Turkish Fuzzy Systems Association,
2(2): 99-121.
29
CHAPTER 3: Optimization in Drilling of Al20%SiCp Metal Matrix Composites
3.1 Coverage
The metal matrix composite (MMC) Aluminum silicon carbide has widespread application in
aerospace, automotive and electronics engineering due to its excellent properties like high
toughness, low weight to volume ratio, high strength, etc. Drilling is one of most common
conventional machining processes being applied on MMCs. For obtaining high product
quality and satisfactory process performance yield it is indeed necessary to control and
optimize several drilling parameters. Taguchi’s philosophy has been mainly concerned with
optimization of single objective function, whereas drilling involves multi-response
characteristics viz. thrust force, torque and circularity at entry and exit; hence exploration of
an appropriate multi-objective optimization technique is certainly essential. To this end, the
present work reports application of (i) PCA-Grey analysis integrated with Taguchi method
and (ii) Grey-TOPSIS combined with Taguchi method in order to obtain appropriate
(optimal) parametric combination in drilling of Al-20%SiCp composites.
3.2 Background and Rationale
Literature depicts that metal matrix composite has widespread applications because of its
excellent properties like high strength, fracture toughness and stiffness. Recently, more
emphasis has been given for development of lighter MMCs using Aluminum matrix and SiC
as reinforcement due to the significant potential improvement in the thrust-to-weight ratio;
suitable for aerospace and automobile applications. Hence, it is important to know the
machinability behavior of these composites. Researchers highlighted the effect of drilling
parameters such as drill speed, feed rate, drill diameter, type of drill etc. on several drilling
30
performance yields during composite drilling and examined to get an optimal parametric
combination to improve the machining performances of these composites as well as to
improve productivity in an economic way.
Sardinas et al. (2006) proposed a multi-objective optimization module for the drilling process
of a laminate composite material. Here, material removal rate and delamination factor were
the two mutually conflicted objectives, optimized by using a micro-genetic algorithm. A
posteriori approach was used to obtain a set of optimal solutions. Finally, the obtained
outcomes were arranged in graphical form (Pareto’s front) and analyzed to make the proper
decision for different process preferences. Ahamed et al. (2010) focused on drilling of Al-5%
SiCp-5% B4Cp hybrid composite with high-speed steel (HSS), PCD, or carbide drills to
explore the viability of the process. It was found that drilling of Al-5%SiC-5%B4C
composites with HSS drills was possible with lower speed and feed combination. The cutting
conditions for minimized tool wear and improved surface finish were also recognized. An
approach for characterization of tool wear and surface integrity was also carried out. Tosun
(2011) carried out statistical analysis of process parameters for surface roughness in drilling
of Al/ SiCp metal matrix composite. Spindle speed, feed rate, drill type, point angle of drill
and heat treatment were taken as cutting parameters for the experiment. It was found that the
feed rate and tool type were more significant factors than other. Hayajneh et al. (2011)
predicted torque and thrust force using feed forward back propagation neural network in dry
drilling of aluminium-copper/silicon carbide composites produced by stir casting method.
Somasundaram et al. (2011) carried out comprehensive analysis on friction drilling of
Al/SiCp metal matrix composites. The composition of work piece, work piece thickness,
spindle speed, and feed rate were taken as the input parameters. Experimental design matrix
was used for analysing the effect of parameters on roundness errors and empirical relation
between the process parameters and roundness error was established using response surface
31
methodology. Analysis of variance was used for analysing the results. The influences of
individual input process parameters on roundness error were analyzed as well. Altunpak et al.
(2012) investigated the influence of cutting parameters on cutting force and surface
roughness in drilling of Al/20%SiC/5%Gr and Al/20%SiC/10%Gr hybrid composites
fabricated by vortex method. The drilling experiments were conducted with carbon coated
cutting tools. The outcomes showed that inclusion of graphite in Al/SiCp reinforced
composite reduced cutting force and found that the feed rate was the main factor influencing
the cutting force in both composites. Huang et al. (2012) experimentally investigated the
influences of the cutting speed and feed rate on the drilling performance of SiCp/Al
composites with 56% SiC particles. Drilling forces, tool wear, and the surface quality of
drilled-hole were taken as the output performance parameters. The result showed that the feed
rate was one of the main cutting parameters that affect the drilling performance, while the
cutting speed had no significant effect on the thrust force. Rajmohan and Palanikumar (2011)
proposed an approach based on grey relational analysis and the Taguchi method in order to
optimize machining parameters with multiple performance characteristics in drilling hybrid
Al356/SiC-mica composites. L9, 3-level orthogonal array was chosen for experiment. Spindle
speed, feed rate, drills and wt% of SiC, were taken as the input parameters and drilling
characteristics were evaluated in terms of thrust force, surface roughness and torque.
Experimental results indicated that the feed rate and the type of drill were the most significant
factors which affect performance. Kumar and Venkataramaiah (2013) focused on selection of
optimal parameters in drilling of Aluminium Metal Matrix Composites (AMMC) using
“Desirable-Fuzzy” approach. Taguchi orthogonal array L27 experimental design was used to
conducting drilling on the AMMC. Drilling performance parameters were evaluated in terms
of thrust force, temperature and surface roughness. Outcomes results were analyzed using
Desirable-Fuzzy approach and optimal parameters combination was identified. Rajmohan and
32
Palanikumar (2013) examined machining characteristics in terms of the thrust force, surface
roughness, burr height, and tool wear using carbide, coated carbide, and polycrystalline
diamond drills in the drilling of hybrid metal matrix composites using the response surface
methodology. Tapkesen et al. (2013) investigated the interactions and effects of the
machining parameters such as cutting speed, feed rate, cutting-tool and material particle
fraction on the thrust force and cutting torque in drilling of aluminum-based composites
reinforced with boron-carbide (B4C) particles with three different types of drills under dry
cutting conditions. Experimental data analysis was carried out with Taguchi’s approach and it
was found that the particle fraction and feed rate were the most affecting factors for the
cutting forces.
The present case study highlights the application of Grey-TOPSIS coupled with Taguchi
method for obtaining optimal machining condition in drilling of MMC composites.
3.3 Experimentation
Work Material
In this work aluminium alloy (Al2265) reinforced with abrasive grade SiC particles of
average size 37μm with 10g in weight made up by the powder metallurgy method, having 25
mm diameter are used for the experimentation.
Tool Material
Drilling tests are performed by using TiN coated HSS twist drills.
Experimental Set Up
Drilling tests have been conducted on CNC drilling machine [MAXMILL 3 axis CNC
machine with FANUC Oi Mate MC Controller, Model No. CNC 2000EG] under dry
conditions. Experimental setup has been shown in Fig. 3.1.
33
Design of Experiment (DOE)
The present study concentrates on the effects of drilling parameters such as drill speed, feed
rate and drill diameter; each varied in three different levels, (as shown in Table 3.1) on
different drilling characteristics namely thrust force, torque and entry-exit circularity of the
drilled hole. In this experimentation, Taguchi based three-level L9 orthogonal array has been
used as shown in Table 3.2.
Response Measurement
Thrust force and torque has been measured with the help of Digital Drilling Tool
Dynamometer [Make: Medilab Enterprises, Chandigarh, INDIA], whereas circularity at inlet
and the exit of the hole have been evaluated by using optical microscope.
3.4 Proposed Methodologies
3.4.1 PCA-Grey Integrated with Taguchi Method
Multiple responses always contain some extent of correlations; the PCA has been initially
performed on the (Signal-to-Noise ratio) S/N values obtained from each response to reduce
the dimension of multiple responses to a less number of uncorrelated indices called principal
components (PCs). Quality loss estimates has been derived based on the deviation of
individual PCs from their ideal value.
Step 1: Collection of Experimental data
Aforesaid machining performance evaluation characteristics viz. thrust force, torque,
circularity at entry and exit has been obtained for each experimental run.
Step 2: Data pre-processing
As optimal value of a quality characteristic is too enormous; experimental data should be
normalized to eliminate these types of effects. Normalization can be done according to the
following equation:
34
Higher-the-Better (HB)
 ŷ  y min 

X i*  
 y max  y min 
(3.1)
Lower-the-Better (LB)
 ŷ  ymax 

X i*  
 ymin  ymax 
(3.2)
(Here y min denotes the lower experimental value of ŷ , the y max represents the upper
experimental value of ŷ .
Step 3: Application of PCA (Liao, 2006; Abhishek, 2012)
PCA
is
a
multivariate
mathematical
procedure
which
explores
an orthogonal
transformation to convert a set of observations of possibly correlated variables into a set of
values of uncorrelated indices called principal components (PCs). Each PC has the property
of explaining the maximum possible amount of variance obtained in the original dataset. The
PCs, which are expressed as linear combinations of the original variables which can be used
for effective representation of the system under investigation, with a lower number of
variables in the new system of variables being called scores, while the coefficient of linear
combination describes each PCs, i.e. the weight of each PCs.
(a) Checking for correlation between each pair of quality characteristics
Let, Qi  X 0* i , X 1* i , X 2* i ,..................., X *m i 
(3.3)
Where,
i  1,2 ,3,.............,n.
It is the normalized series of the i th quality characteristic. The correlation coefficient between
two quality characteristics is calculated by the following equation:
35
 jk 
Cov Q j ,Qk 
(3.4)
 Q j   Qk
here,
j  1,2 ,3 ,......................, n
k  1,2 ,3 ,......................, n
jk
Here,  jk is correlation coefficient,  Q j and  Qk denotes standard deviation of the quality
characteristics j and quality characteristics of k respectively.
(b) Calculation of the principal component score
1) Compute
the
Eigen
k  1,2 ,3,..........n 
value
k
and
the
corresponding
Eigen
vector  k
from the correlation matrix formed by all the quality
characteristics.
2) Compute the principal component scores of the normalized reference sequence and
comparative sequences using the equation shown below:
n
Yi ( k )   X i* ( j ) kj , i  0 ,1,2.........,m , k  1,2 ,3.............., n
(3.5)
j 1
Here, Yi ( k ) is the principal component score of the kth element in the ith series. Let, X i* ( j )
be the normalized value of the jth element in the ith sequence, and  kj is the j th element of
the Eigen vector  k .
(c) Estimation of quality loss 0 ,i ( k )
Loss estimate 0 ,i ( k ) is defined as the absolute value of the difference between desired
(ideal) value and i th experimental value for k th response. If responses are correlated then
instead of using [ X o ( k ) X i ( k ) ]; [ Y0 ( k ) Yi ( k ) ] should be used for computation of
0 ,i ( k ) .
36
 X 0 ( k )  X i ( k ) 
0 ,i  

 Y0 ( k )  Yi ( k ) 
(3.6)
Step 4: Application of Grey Analysis for evaluating overall Grey relation grade:
Individual grey coefficient has been assessed by using as:
 ij 
min  mx
0 i  j   max
(3.7)
Here,
0 i ( j )  y0 ( j  yi ( j )) ,
min  mini minj 0i  j  ,
max  maxi max j 0i  j  , i  1,2 ,........, m
j  1,2 ,....... n
  0 ,1 the distinguishing coefficient, usually,   0.5
The overall grey relational grade computed as:
Ri 
1 n
  ij
n j 1
(3.8)
Step 5: Determine the optimum process variable by optimization OPI using Taguchi method
The optimum process parameter combination ensures highest OPI value. The closeness
coefficient value is optimized using Taguchi method. For calculating S/N ratio
(corresponding to the values of closeness coefficient); Higher-the-Better (HB) criterion is to
be considered. As larger the value of closeness coefficient, better is the proximity to the ideal
solution.
37
3.4.2 Grey-TOPSIS Integrated with Taguchi Method
TOPSIS has been applied to determine the positive-ideal and negative-ideal solution and
thus, closeness coefficient. The closeness coefficient has been treated here as OPI. Optimal
factorial combination (parameter setting) has been evaluated finally by optimizing OPI using
Taguchi method.
Step 1: Determination of S/N ratio for the corresponding responses.
Larger the better
1 n 1
S / N ratio  10 log 10   2
 n i 1 x
ij





(3.9)
1 n

S / N ratio  10 log 10   xij2 
 n i 1 
(3.10)
Smaller the better
i  1,2 ,3,...,n
j  1,2 ,3,...,m
n = no. of experimental data,
x ij = observed response value,
m = no. of responses
Step 2: Normalization of the S/N ratio can be obtain by using the following equation.
Yij 
Yij 
xij  minxij 
maxxij   minxij 
, for larger the better manner
(3.11)
max xij   xij
max xij   min xij 
, for smaller the better manner
(3.12)
Step 3: Application of Grey Analysis for evaluating individual Grey relation grade:
38
Individual grey coefficient has been assessed by using as:
 ij 
min  mx
0 i  j   max
(3.13)
Here,
0 i ( j )  y0 ( j  yi ( j )) ,
min  mini minj 0i  j  ,
max  maxi maxj 0i  j  ,
i  1,2 ,........, m j  1,2 ,....... n
  0 ,1 is the distinguishing coefficient, usually,   0.5
Step 4: Application of TOPSIS for determining OPI:
The individual grey coefficients that have been evaluated are treated as decision matrix in
TOPSIS. Further steps of TOPSIS has been carried out which are earlier discussed in Chapter
2.
Step 5: Parametric optimization of OPI using Taguchi method
The optimum process parameter combination ensures highest OPI value. The closeness
coefficient value is optimized using Taguchi method. For calculating S/N ratio
(corresponding to the values of closeness coefficient); Higher-the-Better (HB) criterion is to
be considered. As larger the value of closeness coefficient, better is the proximity to the ideal
solution.
3.5 Results and Discussions
39
Experimental data presented in Table 3.3 have been analyzed by following aforesaid
procedures. In PCA-Grey method experimental data has been normalized firstly (Table 3.4)
and in Grey-TOPSIS method first S/N ratio is calculated (Table 3.10) then S/N ratio values
has been normalized to convert all response dimensions into a common scale within the range
0 to 1 (Table 3.11). For the thrust force and torque; Lower-is-Better (LB) has been considered
whereas for circularity Higher-is-Better (HB) has been taken in consideration. Now, principal
component analysis has been implemented for checking the correlation among the responses.
Eigen value and Eigen vector has been computed and it has been noticed from Table 3.5 that
first three principal component has major contribution and fourth principal component has
negligible effect. The principal components for each experimental run has been calculated
and shown in Table 3.6. The quality loss has been determined and shown in Table 3.7. After
that, grey relation theory has been implemented to obtain individual grey relation coefficient
which is shown in Table 3.8. Table 3.9 represents the overall grey relation grade; Finally,
Taguchi has been adopted for evaluating the optimal machining condition as N 1000 f 100 d 5
(shown in Fig. 3.2). It has been observed that predicated S/N ratio has highest value among
all computed S/N ratios (Table 3.9). Now, in Grey-TOPSIS method Individual grey
coefficient has been evaluated by using Eq. 3.13 and tabulated in Table 3.12. These
calculated grey coefficients are treated individual alternatives of decision matrix in TOPSIS.
Here, equal weightage has been given to each alternative. The ideal positive and anti-ideal
solution has been determined by using Eq. 2.5, 2.6 and tabulated in Table 3.14. Now,
separation distance measure has been evaluated from both positive ideal and negative ideal
solution by using Eq. 2.7, 2.8 and tabulated in Table 3.15. Over all coefficients have been
evaluated by using Eq. 2.9 and tabulated in Table 3.16. Finally Taguchi method has been
implemented to determine favorable machining condition. The optimal machining condition
40
has been determined as N 500 f 50 D6 and it has been observed from Table 3.16 that predicted
S/N ratio for this setting has higher value as compare to corresponding S/N ratios.
3.6 Concluding Remarks
The present study accomplishes with the two different Multi-Attribute Decision Making
(MADM) methodologies for the optimization of the cutting parameters in drilling of Al20%SiCp composites. Experiments were conducted on Al-20%SiCp composites using TiNcoated carbide drills, the drilling responses were collected under different drilling conditions
for various combination of cutting speed, feed rate, and drill diameter. The objective of the
present work is to investigate the optimal drilling parameters setting based on minimum of
the thrust forces, torque and maximum of the entry and exit circularity in context with by
using two different methodologies i.e. PCA integrated with Grey-Taguchi approach and Grey
integrated with TOPSIS-Taguchi approach.
PCA has been adopted to eliminate the
correlation among the responses, whereas grey relational analysis technique simplifies the
optimization problem by converting the multiple performance characteristics into single
performance characteristics and TOPSIS has the characteristic to evaluate the solution which
is closest to ideal solution. It has been observed that PCA-Grey provides better results as
compare Grey TOPSIS to obtain optimal machining condition (Fig. 3.4).
3.7 Scope for Future Work
In this present research, an emphasis has been given to determine the optimal solution in
drilling of composite by using only one tool material. In future present effort can be extended
to examine the effect of using different tool materials and tool geometry on the quality of
drilled hole and varying different machining parameters at the same time. Also different
41
orientation of fiber in FRP and types of FRP’s and MMCs can be used with or without
consideration of tool wear. Some analytical model can also be developed to evaluate the
output responses.
The limitations of this research are as follows:
1. Interaction effect of machining parameters has been neglected.
2. The composite with 900 fiber orientation has been studied only.
3. Tool geometry variation, tool material has not been considered.
4. Machine tool vibration has been ignored.
5. Tool wear is not considered.
3.8 Bibliography
Abhishek K, Turning of Polymer: A Novel Multi-Objective Approach for Parametric
Optimization, M. Tech. Thesis, 2012.
Ahamed AR, Asokan P, Aravindan S, Prakash MK (2010) Drilling of hybrid Al5%Sicp5%B4Cp metal matrix composites, International Journal of Advanced Manufacturing
Technology, 49(9-12): 871-877.
Altunpak Y, Ay M and Aslan S (2012) Drilling of a Hybrid Al/SiC/Gr Metal Matrix
Composites, International Journal of Advance Manufacturing Technology, 60(11-12):
513-517.
Hayajneh MT, Hassan AM, Mayyas AT and Alrashdan A (2011) Modeling the Drilling
Process of some Al-Mg-Cu Alloys and Al-Mg-Cu/SiC Composite using Artificial
Neural Network, The Online Journal of Science and Technology, 1(1): 18-24.
Huang ST, Zhou L, Chen J and Xu LF (2012) Drilling of SiCp/Al Metal Matrix Composites
with Polycrystalline Diamond (PCD) Tools, Materials and Manufacturing Processes,
27(10): 1090-1094.
42
Kumar GV and Venkataramaiah P (2013) Selection of Optimal Parameters in Drilling of
Aluminium Metal Matrix Composite using Desirable-Fuzzy, Mechanica Confab, 2(5):
14-27.
Liao HC (2006) Multi-response optimization using weighted principal component,
International Journal of Advanced Manufacturing Technology, 27(7-8): 720-725.
Rajmohan T and Palanikumar K (2011) Optimization of Machining Parameters for MultiPerformance Characteristics in Drilling Hybrid Metal Matrix Composites, Journal of
Composite Materials, 46(7): 869-878.
Rajmohan T and Palanikumar K (2013) Modeling and Analysis of Performances in Drilling
Hybrid using D-optimal Design, International Journal of Advance Manufacturing and
Technology, 64(9-12): 1249-1261.
Sardinas RQ, Reis P and Davim JP (2006) Multi-Objective Optimization of Cutting
Parameters for Drilling Laminate Composite Materials by using Genetic algorithms,
Composites Science and Technology, 66(15): 3083-3088.
Somasundaram G, Boopathy SR and Palanikumar K (2011) Modeling and Analysis of
Roundness Error in Friction Drilling of Aluminium Silicon Carbide Metal Matrix
Composite, Journal of Composite Materials, 46(2): 169-181.
Tapkesen A and Kutukde K (2013) Optimization of the Drilling Parameters for the Cutting
Forces in B4C-Reinforced Al-7xxx-Series Alloys Based on the Taguchi, Materials
and technology, 47(2): 169-176.
Tosun G (2011) Statistical Analysis of Process Parameters in Drilling of Al/SiCp Metal
Matrix Composite, International Journal of Advance Manufacturing and Technology,
55(5-8): 477-485.
43
Appendix
Table 2.1: Domain of Experiments
Factors
Unit
Level 1
Level 2
Level 3
Level 4
Spindle Speed
RPM
800
1200
1600
2000
Feed rate
mm/rev
100
150
200
250
Plate Thickness
mm
5
6
7
8
Drill diameter
mm
8
10
_
_
Table 2.2: Design of Experiment (L16) orthogonal array
Drill Speed
Feed rate
Plate Thickness
drill diameter
(RPM)
(mm/rev)
(mm)
(mm)
1.
800
100
5
8
2.
800
150
6
8
3.
800
200
7
10
4.
800
250
8
10
5.
1200
100
6
10
6.
1200
150
5
10
7.
1200
200
8
8
8.
1200
250
7
8
9.
1600
100
7
8
10.
1600
150
8
8
11.
1600
200
5
10
12.
1600
250
6
10
13.
2000
100
8
10
14.
2000
150
7
10
15.
2000
200
6
8
16.
2000
250
5
8
Sl. No.
44
Table 2.3: Experimental Data
Torque
Thrust
Ra
(N-m)
(N)
(μ-m)
1
2.943
0.99081
2
6.867
3
Sl. No.
Fin
Fout
5.098
1.1772395
1.172444785
1.14777
5.036
1.1881515
1.177239452
10.4967
1.15758
8.901667
1.2097903
1.175348039
4
17.7561
1.51074
11.30967
1.1709568
1.193944732
5
10.3986
0.81423
5.453
1.1791573
1.198997318
6
13.6359
0.84366
4.816667
1.259549
1.297853424
7
7.9461
1.40283
3.272667
1.1963851
1.109518919
8
13.6359
1.57941
4.471
1.2203253
1.186828785
9
3.7278
0.74556
6.282333
1.1867957
1.196385052
10
1.2753
0.93195
7.266333
1.1282016
1.061241587
11
7.7499
0.96138
8.732333
1.2403968
1.198309532
12
7.4556
0.86328
5.244333
1.251904
1.220927131
13
16.9713
0.42183
10.56633
1.2748655
1.216959131
14
10.4967
0.48069
8.170667
1.1973572
1.159052785
15
3.8259
0.87309
4.725
1.1868288
1.220325318
16
12.8511
1.03986
6.964667
1.2059744
1.206933318
Table 2.4: Normalized Decision Matrix
Sl. No.
Torque
Thrust
Ra
Fin
Fout
1
0.070683392
0.23956731
0.18167812
0.244206972
0.246715508
2
0.164927914
0.27751857
0.17946862
0.246470561
0.247724441
3
0.252104097
0.27989053
0.31722991
0.250959327
0.247326434
4
0.426456464
0.36528086
0.40304424
0.242903693
0.251239704
5
0.249747984
0.19687215
0.1943293
0.244604815
0.252302911
6
0.327499715
0.20398801
0.17165222
0.261281293
0.273105028
7
0.190845158
0.33918937
0.11662848
0.248178542
0.233474128
8
0.327499715
0.38188453
0.15933363
0.253144719
0.249742308
9
0.089532296
0.18026847
0.22388435
0.246189327
0.251753216
45
10
0.03062947
0.22533559
0.25895129
0.234034539
0.223315213
11
0.186132932
0.23245145
0.31119534
0.257308351
0.252158181
12
0.179064592
0.20873192
0.18689301
0.259695409
0.256917563
13
0.407607559
0.10199401
0.37655374
0.264458549
0.256082584
14
0.252104097
0.11622573
0.29117917
0.248380207
0.243897452
15
0.091888409
0.21110387
0.16838547
0.246196186
0.256790924
16
0.308650811
0.25142708
0.24820078
0.250167756
0.253972869
Weightage
0.2
0.2
0.2
0.2
0.2
Table 2.5: Weighted Normalized Matrix
Sl. No.
Torque
Thrust
Ra
Fin
Fout
1
0.014136678
0.047913463
0.036335624
0.04884139
0.0493431
2
0.032985583
0.055503714
0.035893723
0.04929411
0.04954489
3
0.050420819
0.055978105
0.063445983
0.05019187
0.04946529
4
0.085291293
0.073056171
0.080608849
0.04858074
0.05024794
5
0.049949597
0.03937443
0.03886586
0.04892096
0.05046058
6
0.065499943
0.040797602
0.034330443
0.05225626
0.05462101
7
0.038169032
0.067837873
0.023325696
0.04963571
0.04669483
8
0.065499943
0.076376906
0.031866727
0.05062894
0.04994846
9
0.017906459
0.036053695
0.044776871
0.04923787
0.05035064
10
0.006125894
0.045067119
0.051790259
0.04680691
0.04466304
11
0.037226586
0.046490291
0.062239067
0.05146167
0.05043164
12
0.035812918
0.041746383
0.037378601
0.05193908
0.05138351
13
0.081521512
0.020398801
0.075310747
0.05289171
0.05121652
14
0.050420819
0.023245145
0.058235834
0.04967604
0.04877949
15
0.018377682
0.042220774
0.033677093
0.04923924
0.05135818
16
0.061730162
0.050285416
0.049640157
0.05003355
0.05079457
46
Table 2.6: Positive Ideal Solution and Negative Ideal Solution
Torque
Thrust
Ra
Fin
Fout
A+
0.006125894
0.020398801
0.023325696
0.04680691
0.04466304
A-
0.085291293
0.076376906
0.080608849
0.05289171
0.05462101
Table 2.7: Conflict between each alternative and the positive and the negative ideal solution
Cos  
Cos  
1.
0.956784401
0.88288183
2.
0.913967031
0.941753645
3.
0.85893116
0.987059298
4.
0.75420841
0.999410383
5.
0.889306762
0.964534138
6.
0.84795811
0.953349907
7.
0.860547359
0.916868942
8.
0.7970471
0.956446437
9.
0.965862544
0.897162582
10.
0.933085585
0.866712618
11.
0.901531141
0.962307259
12.
0.937588695
0.940829538
13.
0.766488592
0.939852085
14.
0.867479458
0.94743711
15.
0.968353392
0.888921559
16.
0.845382672
0.986782609
Sl. No.
47
Table 2.8: Overall Performance Index (OPI)
Sl.
No.
OPI by TOPSIS
OPI by Deng’s Similarity
Method
1.
0.735714028
0.705737476
2.
0.609318215
0.682315862
3.
0.388134092
0.658213474
4.
0.059093032
0.625483138
5.
0.567107
0.671103732
6.
0.487739182
0.663120971
7.
0.567172173
0.675022134
8.
0.391085254
0.648413601
9.
0.744386219
0.704364506
10.
0.706415709
0.704365556
11.
0.512669447
0.67461764
12.
0.649762985
0.688031776
13.
0.380252326
0.643475641
14.
0.544262978
0.6695644
15.
0.760079881
0.706816501
16.
0.406552098
0.654691051
Table 2.9: Corresponding S/N Ratios (of OPIs) and Predicted S/N Ratios
Predicted
Sl. No.
TOPSIS
Deng’s
Predicted
S/N Ratio
Similarity
S/N Ratio
(Deng’s
Method
(TOPSIS)
Similarity
Method)
1.
-2.665819266 -3.027136405
2.
-4.303116778 -3.320290647
3.
-8.220364172 -3.632664631
4.
-24.56927458 -4.075687874
5.
-4.926699846 -3.464206925
6.
-6.23624708
2.57546
-2.76218
-3.568144746
48
7.
-4.925701694 -3.413639726
8.
-8.154571168 -3.762957687
9.
-2.564033512 -3.044050735
10.
-3.018793036 -3.044037795
11.
-5.803251274 -3.418846144
12.
-3.744900657 -3.247830082
13.
-8.398562404 -3.829357779
14.
-5.283824123 -3.484152901
15.
-2.382815263 -3.013866409
16.
-7.817675863 -3.679271905
Table 3.1: Domain of Experiments
Factors
Unit
Level 1
Level 2
Level 3
Spindle Speed (N)
RPM
500
750
1000
Feed rate (f)
mm/min
50
100
150
Drill diameter (D)
mm
5
6
8
Table 3.2: Design of Experiments
Sr. No.
Speed (RPM)
Feed (rev/mm)
Diameter (mm)
1
500
50
5
2
500
100
6
3
500
150
8
4
750
50
6
5
750
100
8
6
750
150
5
7
1000
50
8
8
1000
100
5
9
1000
150
6
49
Table 3.3: Experimental Data
Sl. No.
Thrust force (N)
Torque (Nm)
Circularity (in)
Circularity (out)
1.
1.5092
2.45
0.899563319
0.92139738
2.
3.136
2.4206
0.925190311
0.914893617
3.
3.6162
6.664
0.9269264
0.910740691
4.
4.116
1.8718
0.893270188
0.923538073
5.
2.499
6.272
0.969112282
0.969411255
6.
3.6848
6.86
0.894751739
0.941456307
7.
2.254
7.938
0.9328
0.89528
8.
2.1364
6.958
0.95610766
0.989500022
9.
2.0482
2.254
0.882489704
0.941998336
Table 3.4: Normalization of Experimental Data
Sl. No.
Thrust force
Torque
Ideal
1
1
1
1
1.
1
0.904684976
0.197101
0.277196
2.
0.37593985
0.909531502
0.49295
0.208168
3.
0.191729323 0.210016155
0.512992
0.164091
0.124451
0.299916
4.
0
1
Circularity (in) Circularity out
5.
0.620300752 0.274636511
1.00000
0.786789
6.
0.165413534 0.177705977
0.141555
0.49009
7.
0.714285714
0.580799
0
8.
0.759398496 0.161550889
0.849873
1
9.
0.793233083 0.936995153
0
0.495843
0
50
Table 3.5: Eigen value, Eigen vector, AP and CAP
PC1
PC2
PC3
PC4
Eigen value
1.8911
1.0644
0.7134
0.0657
Eigen vector
 0 .262
0. 531
0. 645
0. 482
0.777
0.508
0.152
 0.340
0.559
 0.322
 0.076
0.760
 0.126
.0.597
 0.745
0.271
AP
0.473
0.266
0.178
0.083
CAP
0.473
0.739
0.917
1.000
Table 3.6: Major Principal Components for L9 experimental run
Sl. No.
PC1
PC2
PC3
Ideal
1.396
1.097
0.921
1.
0.479126
1.172293
0.46338
2.
0.802755
0.758298
0.038025
3.
0.471257
0.277846
0.125274
4.
0.75583
0.424945
-0.10352
5.
1.007548
0.505981
0.780275
6.
0.37855
0.073687
0.396955
7.
0.187473
0.643281
0.355145
8.
0.916989
0.461301
1.067894
9.
0.528712
0.923748
0.518546
Table 3.7: Quality loss ( ok )
01
02
03
1.
0.916874
0.075293
0.45762
2.
0.593245
0.338702
0.882975
3.
0.924743
0.819154
0.795726
4.
0.64017
0.672055
1.024522
5.
0.388452
0.591019
0.140725
6.
1.01745
1.023313
0.524045
Sl. No.
51
7.
1.208527
0.453719
0.565855
8.
0.479011
0.635699
0.146894
9.
0.867288
0.173252
0.402454
Table 3.8: Individual grey coefficients (  ij )
1
2
3
1.
0.916874
0.075293
0.45762
2.
0.593245
0.338702
0.882975
3.
0.924743
0.819154
0.795726
4.
0.64017
0.672055
1.024522
5.
0.388452
0.591019
0.140725
6.
1.01745
1.023313
0.524045
7.
1.208527
0.453719
0.565855
8.
0.479011
0.635699
0.146894
9.
0.867288
0.173252
0.402454
Sl. No.
Table 3.9: Over all Grey coefficient ( Ri ), Corresponding S/N ratio and Predicted S/N ratio
Sl. No.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Ri
SNRA1
PSNRA1
0.775293
0.662411
0.529844
0.572828
0.844098
0.541545
0.587097
0.806204
0.748483
-2.21068
-3.57745
-5.51704
-4.83951
-1.47214
-5.32731
-4.62580
-1.87111
-2.51636
-1.34604
52
Table 3.10: Corresponding S/N ratio of experimental data
Sl. No.
Thrust force
Torque
Circularity (in)
Circularity (out)
1.
-3.574935931
-7.783321687
-0.919365237
-0.71106054
2.
-9.92752108
-7.678460579
-0.67537848
-0.772588047
3.
-11.16504884
-16.47469977
-0.659094969
-0.812105183
4.
-12.28950732
-5.445188859
-0.980343198
-0.69090392
5.
-7.955325123
-15.94812099
-0.272518048
-0.269838847
6.
-11.32827841
-16.72648231
-0.965948977
-0.523996616
7.
-7.059078234
-17.99422189
-0.604229252
-0.960822345
8.
-6.593651386
-16.84968849
-0.389864048
-0.091683836
9.
-6.227447236
-7.059078234
-1.085807056
-0.518997287
Table 3.11: Normalized S/N ratio
Sl. No.
Thrust force
Torque
Circularity (in)
Circularity (out)
1.
0
0.18632
0.795347
0.712633
2.
0.728961284
0.177964
0.495347
0.783424
3.
0.87096801
0.878913
0.475325
0.828891
4.
1
0
0.870324
0.689441
5.
0.502651134
0.836952
0
0.204979
6.
0.889698659
0.898977
0.852625
0.497404
7.
0.399806502
1
0.407864
1
8.
0.346398614
0.908795
0.144286
0
9.
0.304376565
0.128607
1
0.491652
53
Table 3.12: Individual Grey Coefficient
Sl. No.
Thrust force
Torque
Circularity (in)
Circularity (out)
1.
0.333333
0.38061
0.709569375
0.63502781
2.
0.648476
0.378204
0.497684374
0.697762967
3.
0.794872
0.80504
0.487959786
0.745035787
4.
1
0.333333
0.794059488
0.616858558
5.
0.501329
0.754093
0.333333333
0.38609408
6.
0.819267
0.831915
0.772350444
0.498705251
7.
0.454466
1
0.457818386
1
8.
0.433425
0.84573
0.368809278
0.333333333
9.
0.418192
0.364593
1
0.495860423
Table 3.13: Weighted Normalized matrix (TOPSIS)
Sl. No.
Thrust force
Torque
Circularity (in)
Circularity (out)
1.
0.083333
0.095152531
0.177392344
0.15875695
2.
0.162119
0.094551107
0.124421093
0.17444074
3.
0.198718
0.201260117
0.121989946
0.18625895
4.
0.25
0.083333333
0.198514872
0.15421464
5.
0.125332
0.188523165
0.083333333
0.09652352
6.
0.204817
0.207978768
0.193087611
0.12467631
7.
0.113616
0.25
0.114454597
0.25
8.
0.108356
0.211432616
0.092202319
0.08333333
9.
0.104548
0.091148176
0.25
0.12396511
Table 3.14: Positive and negative ideal solution
Thrust force
Torque
Circularity (in)
Circularity out
A+
0.083333
0.083333333
0.198514872
0.25
A-
0.25
0.25
0.083333333
0.08333333
54
Table 3.15: Separation Distance
Sr. No.
S+
S-
1
0.094399
0.257471
2
0.132409
0.204637
3
0.192716
0.130742
4
0.192231
0.214636
5
0.222824
0.139626
6
0.214547
0.132524
7
0.189106
0.217593
8
0.236888
0.147068
9
0.13801
0.275352
Table 3.16: Overall Performance Index (OPI) and Predicted S/N Ratio
Sl. No.
Di
S/N ratio of OPI
1.
0.731722225
-2.71308
2.
0.607148551
-4.33410
3.
0.404200955
-7.86805
4.
0.527534356
-5.55499
5.
0.385228113
-8.28564
6.
0.381835493
-8.36247
7.
0.535022829
-5.43255
8.
0.383034125
-8.33525
9.
0.666128944
-3.52883
Predicted S/N
Ratio
-1.91904
55
Fig. 2.3: GFRP epoxy work pieces after machining
Fig. 2.4: Drill bits  8 ,10 used during experimentation
56
Mean of SN ratios
Fig. 2.5: Evaluation of optimal parametric combination by using TOPSIS based Taguchi
Mean of SN ratios
method  N 1600 f 100 t 6 d 8 
Fig. 2.6: Evaluation of optimal parametric combination by using Deng’s Similarity Based
Method in conjugation with Taguchi approach N 1600 f100 t 6 d 8 
57
Spindle
Drill bit
Work piece
Vice
Dynamometer
Mean of SN ratios
Fig. 3.1: Experimental setup for drilling of Al20%SiCp Composite
Fig. 3.2: Evaluation of optimal parametric combination by PCA-Grey integrated with
Taguchi methodology
58
Mean of SN ratios
Fig. 3.3: Evaluation of optimal parametric combination by Grey -TOPSIS integrated with
Taguchi methodology
0.9
Overall Performance Index
0.8
0.7
0.6
0.5
PCA Grey
0.4
Grey TOPSIS
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
Fig. 3.4: Graphical comparison between PCA-Grey and Grey-TOPSIS integrated with
Taguchi method on basis of OPIs
59
List of Publications
1. Vikas Sonkar, Kumar Abhishek, Saurav Datta, Siba Sankar Mahapatra, “MultiObjective Optimization in Drilling of GFRP Composites: A Degree of Similarity
Approach”,
International
Conference
on
Materials
Processing
and
Characterisation (ICMPC 2014), organized by Department of Mechanical
Engineering, Gokaraju Rangaraju Institute of Engineering and Technology,
Hyderabad, Andhra Pradesh (India).
2. Vikas Sonkar, Kumar Abhishek, Saurav Datta, Siba Sankar Mahapatra,
“Optimization in drilling of Al-20%SiCp Composites by using Grey TOPSIS”,
International Mechanical Engineering Congress (IMEC 2014), June 13-15, 2014,
organized by Department of Mechanical Engineering, National Institute of
Technology, Tiruchirappalli, Tamil Nadu (India).
3. Kumar Abhishek, Vikas Sonkar, Saurav Datta, Siba Sankar Mahapatra,
“Optimization in drilling of MMC Composites: A case research”, Recent Advances
in Manufacturing (RAM- 2014), 26-28 June, 2014, organized by Department of
organized by Department of Mechanical Engineering, National Institute of
Technology, Surat, Gujarat (India). (Under Review)
60